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Publications Influence

RIGIDITY OF GRADIENT RICCI SOLITONS

- P. Petersen, W. Wylie
- Mathematics
- 16 October 2007

We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×GRk where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the… Expand

171 17- PDF

On the classification of gradient Ricci solitons

- Peter Petersen, W. Wylie
- Mathematics
- 8 December 2007

We show that the only shrinking gradient solitons with vanishing Weyl tensor and Ricci tensor satisfying a weak integral condition are quotients of the standard ones S n , S n 1 R and R n . This… Expand

134 10- PDF

COMPARISON GEOMETRY FOR THE BAKRY-EMERY

For Riemannian manifolds with a measure (M, g, e f dvolg) we prove mean curvature and volume comparison results when the ∞Bakry-Emery Ricci tensor is bounded from below and f or |∇f | is bounded,… Expand

36 9

A warped product version of the Cheeger-Gromoll splitting theorem

- W. Wylie
- Mathematics
- 11 June 2015

We prove a new generalization of the Cheeger-Gromoll splitting theorem where we obtain a warped product splitting under the existence of a line. The curvature condition in our splitting is a… Expand

29 8- PDF

On the classification of warped product Einstein metrics

- Chenxu He, P. Petersen, W. Wylie
- Mathematics
- 26 October 2010

The question of when an Einstein metric can be written as a warped product is posed in the text Einstein metrics by Besse. Recently, there have been some interesting results about these spaces found… Expand

83 5- PDF

On Gradient Ricci Solitons with Symmetry

- P. Petersen, W. Wylie
- Mathematics
- 18 October 2007

We study gradient Ricci solitons with maximal symmetry. First we show that there are no nontrivial homogeneous gradient Ricci solitons. Thus, the most symmetry one can expect is an isometric… Expand

111 4- PDF

On the geometry of Riemannian manifolds with density

- W. Wylie, Dmytro Yeroshkin
- Mathematics
- 25 February 2016

We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplacian, as the… Expand

14 4- PDF

Stochastic principles governing alternative splicing of RNA

TLDR

15 2- PDF

Gradient shrinking Ricci solitons of half harmonic Weyl curvature

- Jia-Yong Wu, P. Wu, W. Wylie
- Mathematics
- 27 October 2014

Gradient Ricci solitons and metrics with half harmonic Weyl curvature are two natural generalizations of Einstein metrics on four-manifolds. In this paper we prove that if a metric has structures of… Expand

17 2- PDF

Positive weighted sectional curvature

- L. Kennard, W. Wylie
- Mathematics
- 6 October 2014

In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We… Expand

15 2- PDF